Status of Neutrino Physics
Vernon Barger
SLAC Summer InstituteJuly 27, 2006
Outline
• The 3ν paradigm• Neutrino oscillations
– ATM, solar, reactor, future
• Absolute mν
• Neutrino cosmology– BBN, CMB, galaxy surveys
• New ideas– MaVaNs
Pre 1998: Standard Model mν = 0
1998-present: The Neutrino RevolutionNeutrino flavors oscillate ⇒ neutrinos have massNew SM: minimal SM extensions
With L-conservation add νR: Dirac ν (ν≠νc)
With L not conserved: Majorana ν (ν=νc)
L = LSM − mνν Lν R + h.c.
L = LSM −12
mνν Lν Lc + h.c.
Note: oscillations give no information on:Dirac vs. Majoranaabsolute ν-mass (only probe )mi
2 − m j2
How do oscillations occur?
source detector
νμ
μ+ τ−
ντlong distance
νj
Lifestyle of a muon neutrino
PRODUCTION: born as a flavor (e.g. νμ)
PROPAGATION: travels as mass eigenstates
DETECTION: dies as a flavor (νμ or ντ)
QM : e− i(E j − pL ) ≅ e− i
m j2
2EL ( L ≅ ct )
Weak charged currents connect flavor eigenstates
να ⟩ α = e,μ,τ
The flavor eigenstates are mixtures of mass eigenstates
ν i⟩ i =1,2,3
The mixing is described by a unitary matrix V
να ⟩ = Vαj* ν j ⟩
Probability of detecting flavor β at a discrete distance L from a source that
produced flavor α
P(να → ν β ) = δab − 4 Re[Vαi*VβiVαjVβj
* ]sin2 Δ ijj≠ i
n
∑
+2 Im[Vαi*VβiVαjVβj
* ]sin(2Δ ij )j≠ i
n
∑
Oscillation argument
Δ ij =1.27δmij
2
eV2L / E
km/GeVδmij
2 ≡ mi2 − m j
2
Data have probed sub-eV2 neutrino mass-squared differences
Three Neutrino Paradigm
The 3ν mixing matrix
atm unknown solar 0νββ(Majorana phases)
3 angles (θa, θs, θx)1 Dirac phase (δ)2 Majorana phases (φ2, φ3)δ≠0 and sx≠0 ⇒P(ν α ↔ ν β ) ≠ P(να ↔ ν β ) CP-violation
Empirically, and are very different and their oscillations are nearly decoupled (θx small)
δma2 δms
2
Effective 2-neutrino oscillations good first approximationwith one δm2 is dominant
P(να → ν β ) ≅ sin2 2θ sin2 Δ
P(να → να ) ≅1− sin2 2θ sin2 ΔΔ =
δm2L4E
Recap of the evidence for neutrino oscillations
Atmospheric neutrinos
νμ↔νμ depletion observed ( > 15σ)νμ↔νe excluded ( > 5σ)*νμ↔ντ inferred
Vacuum oscillations
P(ν μ → ν μ ) = sin2 2θa sin2 δma2L
4Eν
δma2 ≈ 2 ×10−3 eV2
Large mixing θa = 45 ± 10o 95% C.L.
∗ θx smallAlso from CHOOZ reactor experiment for disappearance sin2θx < 0.05
ν e ↔ ν e
Atmospheric Neutrinos
Atmospheric ν oscillations ν μ ↔ ν μ,ν μ ↔ ν μ
SuperK data
Accelerator Confirmation of ATM oscillationsK2K: νμ beam from KEK to Kamiokande
L = 250 kmMINOS: νμ beam from Fermilab to Soudan
L = 735 km
Confirmation of ATM oscillationsConfirmation of ATM oscillations
K2K 2006: spectral distortion
Solar neutrinos
ν e ↔ ν e depletion observed (> 7σ )
Interior of sun well-modeled and νe flux predicted
p + p → 2H + e+ + νe7Be + e– → 7Li + νe
8B → 8Be + e+ + νe
Experimental proof of solar νe oscillations from the Sudbury Neutrino Observatory (SNO)
Measured CC
SNO sees νe depletion
Measured NC
SNO sees predicted solar neutrino flux
So the “missing” νe were converted to νμ and ντ by oscillations!
νx νx νx = νe , νμ, ντνe
W
e
p
pd
Z n
d p
Essential WrinkleEssential WrinkleNeutrinos created in the solar core travel through dense matter to get out
The νe scatter from electrons in the matter differently fromother neutrinos, creating a different index of refraction for νe
Wolfenstein (1976)
(charged current) (neutral current)
Resonance can occur in νe oscillations!
A = 2 2GF Ne Eν Barger,Pakvasa,Phillips,Whisnant (1980)
sin22θm enhancement for δm2 > 0
Matter resonance proposed as explanation of the solar neutrino deficit (MSW)
But global fits select LMA solution
Neutrinos propagate adiabatically through the matter resonance- no level crossing
δms2 ≈ 6 ×10−5 eV2
θs ≈ 33o
Mikheyev-Smirnov (1985)
Natural: small θs amplified by resonance (SMA solution)
C. Gonzalez-Garcia et al.
vacuum average
VB, Marfatia, Whisnant, 2005
PH = cos4θx sin2θs
+ sin4θx
matter dominated
data points assume SSMfluxes for Low, Intermediateenergies
PL = cos4 θx 1− 12 sin2 2θs( )
SuperK, SNOChlorineGallium
P(νe→ νe)
p + p → 2H + e+ + νe7Be + e– → 7Li + νe
8B → 8Be + e+ + νe
KamLAND reactor confirmation of LMAν e ↔ ν e at L ~ 180 km, Eν ~ few MeVν e + p → n + e+
assume CPT : P(ν e → ν e ) = P(ν e → ν e )[ ]
2004: Energy Distortion
Solar + KamLAND
Fogli et al. (2005)
State composition for two possible mass orderings
NH IH
Still Unknown
θx
sign(δma2)
Can be resolved by earth matterEffects on νμ→νe oscillations in Earthprovided that θx≠ 0
ν μ → ν e oscillations at δma2
scale not seen; θx small for unknown reason
Enhance P(ν μ → ν e ) and suppress P(ν μ → ν e )
or vice versa depending on sign(δma2)
Summary of knowns and unknowns3ν
observablePresent
knowledge (1σ)
|δma2 |
sign(δma2)
|δms2 |
sign(δms2)
tan2 θa
tan2 θs
sin2 θx
δMajorana/Dirac
φ2,φ3
mν
2.05 ±0.40.4( )×10−3 eV2
unknown
8.0 ±0.50.4( )×10−5 eV2
+
1.00−0.27+0.38
0.45−0.05+0.05
< 0.045
unknownunknownunknown
mν∑ ≤ 0.6 eV (cosmology)
P(ν μ → ν e ) ≠ P(ν μ → ν e )
ΔP ∝δms
2
δma2
⎛
⎝ ⎜
⎞
⎠ ⎟ sin2θx sinδ
Both and oscillations mustcontribute to have CP violation
δms2 δma
2
δ
The ultimate goal of long-baseline experiments is to determine the CP-violating phase δ
8-fold parameter degeneracy
Can be resolved with longbaseline experiments
sign(δma2)
(δ,θx )
(θa, π2
−θa )
Must distinguish intrinsic CP-violation fromfake CP-violation due to matter effects
Barger, Marfatia, Whisnant
Mena and Parke
sin2 2θx sin2 2θx
T2HK and NOνA are complementaryCombining results from 2 long-baseline experiments eliminates fake solutions caused by matter effects
Tri-bi maximal mixing(θa = π/4, θs = π/6, θx = 0)
Harrison, Perkins, Scott
V =
26
13
0
−16
13
12
−16
13
−12
⎛
⎝
⎜ ⎜ ⎜ ⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ ⎟ ⎟ ⎟
Consistent with all present dataAlas, if true, • No dependent Earth matter effects
• No CP violation
δma2
Theoretical basis uncertain: models proposed
3 neutrino paradigm in great shape with one possible exception:
Oscillations to sterile neutrinos invoked:
LSND evidence for ν μ ↔ ν e oscillations with
δmLSND2 ~ 1 eV2 and θLSND ~ 10−2
Active333333
Sterile21111-
extra-
CPT violationMaVaNs
Sterile decayExtra dim
Quantum decoherence
Fermilab MiniBooNE experiment willtest these speculative models
Life in Hellby Matt Groening
Absolute neutrino mass
• 3H beta decay: Mainz experiment
mβ = Vei2 mν i
2∑( )1
2 < 2.2 eV
Future: KATRIN sensitivity down to 0.3 eV
• Neutrinoless nuclear double beta decay
N(n, p) → N(n − 2, p + 2) + 2e−
Heidelberg-Moscow experiment:
mee = Vej2mν j∑
Occurs only if neutrinos are Majorana ν i = ν i
(usual theoretical prejudice)
Upper limit: mee < 0.35 eV at 95% C.L.mee = 0.1 - 0.9 eV controversial detection
IH predicts lower limit on mee
Atre et al. (2005)
Future U.S. neutrino program goals
Nu-SAG charges (2006)[Neutrino Scientific Assesment Group]
1. Reactor experiment with θx sensitivity down to
Daya Bay (Double Chooz)
2. Neutrinoless nuclear double beta decay experiments (different nuclei)
CUORE, EXO, MajoranaGERDA, Super Nemo, Moon
3. Accelerator experiment with θx sensitivity down to
and sensitivity to the mass-hierarchy through matter effectsT2K (Japan), NOVA (US)
sin2 2θx = 0.01 (now sin2 2θx < 0.19)
sin2 2θx = 0.01
Double Chooz (approved)
sin22θx sensitivity:
0.02 at 90% C.L.
Reactor
optimal distance ~1.7 km
monitor flux measureat osc minimum
Measure θx via disappearance with two detectors
Reactor experiments
Geer (2006)
The race for θx discovery
Off-axis neutrino beamsSuperbeamsNeutrino Factory
Approximate discovery reaches in sin2 2θx
Current limit 10−1
Reactor 10−2
Conventional π-beam 10−2
Superbeam 3 × 10−3
NuFact (entry level) 5 × 10−4
NuFact (high performance) 5 × 10−5
β-beams comparable to NuFact (10−3 -10−4)
Pursue θx as small as we need to go!
β-beams+ new detector technologies
νμ+ or μ−
4He primordial abundance in BBN
Yp ≅2nn /np
1+ nn /np T freeze
nn /np ~ e−(mn −m p )/T freeze , Tfreeze ~ 1 MeV
Extra light neutrinos
would speed up expansion
ΔNν = Nν − 3
Hnew
Hstd
= 1+743
ΔNν
⎛ ⎝ ⎜
⎞ ⎠ ⎟
12 H = Ý a /a
giving earlier n / p freeze - out and higher 4He abundance for ΔNν > 0
Primordial Neutrinos
Revised estimates of primordial helium abundance
Yp = 0.249 ± 0.009 Olive-Skillman (2004)
Yp = 0.250 ± 0.004 Fukugita-Kawasaki (2006)
• Preferred Nν consistent with 3• Neutrino contribution to radiation density established (lower bound on Nν)• Nν = 4 allowed
LSND neutrino thermalizes giving Nν = 4
1.7 ≤ Nν ≤ 4.5 at 95% C.L. Cyburt et al. (2004)
BBN + Yp + ηCMB (baryon / photon ratio):
Neutrino counting with CMB
Power spectrum is sensitive to Nν
But Nν correlated with ΩMh2
Analyze CMB data along with data that constrain ΩM
CMBWMAP 3- year
+ other CMBΩΛ + ΩM( )h2
SNSupernova
gold + SNLSΩΛ − ΩM( )h2
LSSGalaxy clustering
SDSS & 2dFΩΛ ,ΩM( )h
BAO Luminous red galaxies ΩM h2
LYA Lyman -α forest ΩM h
Nν = 3.29−2.18+0.45• Spergel et al (2006)
WMAP-3 + other CMB+ SN + LSS
• Seljak et al (2006)… + LYA + BAO
• Hannestad et al (2006)CMB + LSS
• Barger et al (2003)WMAP-1 + H0
Nν (with Σmν = 0) at 2σ
0.9 < Nν < 8.3
Nν = 5.1−1.7+2.1
2.7 < Nν < 4.6
Excellent accord of BBN (20 min), CMB (380,000 years) and LSS (10 Gyr)
Nν = 4 OK
(Nν=3 allowed only at 3σ)
Neutrino Mass from the CMB
Massive neutrinos slow the growth of small scale structureJoint analyses of CMB and LSS data constrains Σmν
(1σ)• Spergel et al (2006)
• Seljak et al (2006)
• Hannestad et al (2006)
• Barger et al (2004)WMAP-1 + LSS + H0+ other CMB
Σmν (for Nν = 3)
< 0.75 eV (2σ)
(2σ)
(2σ)< 0.62 eV
< 0.17 eV
< 0.68 eV
Mass varying Neutrinos (MaVaNs)Motivation: dark energy density (2x10-3 eV)4 is comparable to neutrino mass splitting scale
δmν2 ~ (10−2 eV)2
Proposal: relic neutrinos interact via a new scalar field φ(the “acceleron”) and form a negative pressure fluid that causes the cosmic acceleration. Fardon, Nelson, Weiner (2005)
Very speculative, but very interesting!
New Ideas:
Mechanism: sterile neutrino interacts through Yukawa couplings to the acceleron φ
A prototype low energy effective Lagrangian
L = mDνN + κφNN + h.c.+ V φ( )
If κφ >>mD see-saw givesL =
mD2
κφν 2 + h.c.+ V φ( )
Effective φ-dependent neutrino mass at late times:
mν (φ) = mD2 /κφ
ν = left - handed active neutrino N = right - handed sterile neutrino κ = Yukawa coupling
FNW Dark Energy Scenario• Neutrino mass a dynamical field which is a function
of the acceleron field: mν(φ)• Dark energy is the sum of the neutrino energy
density and the scalar potential of the acceleron
ρDE = ρν + V (φ) Non - Rel : ρν = mν nν
• .ρDE is stationary with respect to mν
∂ρDE
∂mν
= 0
So, mν tracks the instantaneous minimum of the DE
Solution of stationary condition gives mν as a function of T for a given V(φ)
MaVaNs implications for neutrino mass in particle physics
Complicated interplay that remains tobe quantitatively explored
Background mν declines with redshift
But, a higher vacuum mν causes clustering and thecorresponding higher neutrino number densitylowers the effective neutrino mass
Extension: φ also couples to matter, then localneutrino mass could vary with local mass density
Phenomenology: MaVaN effects in addition to standard matter effects in neutrino oscillations
Neutrinos would be most massive in a vacuum
Revisit solar neutrinos (high densities)
HMaVaN =1
2EV
(m1 − M1(r))2 M3(r)2
M3(r)2 (m2 − M2(r))2
⎛
⎝ ⎜
⎞
⎠ ⎟ V +
V = 2 × 2 mixing matrix
Hmatter =1
2E2 2GF Eν ne (r) 0
0 0
⎛
⎝ ⎜
⎞
⎠ ⎟ , ne ∝e−r / r0
ne0 = electron density at production point
Introduce parameterization
Mi = μine (r)
ne0
⎛
⎝ ⎜
⎞
⎠ ⎟
k
μi,k free parameters
Two-neutrino framework (νe, νμ)
VB, Huber, Marfatia (2005)
MaVaN oscillations with exotic matter effects comparableto standard matter effects allowed
• propagation inside sun still adiabatic - solar survivalprobability independent of how the neutrino masses depend on density
• can be tested with MeV and lower energy solarneutrino experiments (KamLAND, Borexino)
• are consistent with other neutrino oscillationexperimental data (KamLAND, day night Earth effects,atm neutrino oscillations)
Why are neutrinos so light?
Favored explanation — the light neutrino masses are pushed down by mixing with very heavy neutrinos
that are present in Grand Unified Theories
If so, light neutrinos are a “window” to new physicsat energies that are inaccessible in the laboratory
mlight ≅m2
M
0 mm M
⎛
⎝ ⎜
⎞
⎠ ⎟
mheavy ≅ M
Eigenstates are dominantly Majorana
Matter-antimatter asymmetry from processes that violate CP in the early universe
Baryon number asymmetry could be associated with lepton number asymmetry through SM sphaleron processes
Lepton asymmetry from decays of heavy right-handed neutrinos (CP-violating phase)
≠N N
H H
l l
Leptogenesis?
Sensitive new probes coming:New terrestrial experiments
• β, 0νββ, reactor, long baseline experimentsNew cosmology observations
• Planck CMB
Neutrino mass changes with density?Neutrino connection to dark energy?
New ideas to be explored
Outlook
The exciting physics of neutrinos is still unfolding.